# CSEC Mathematics: Matrices- Determinants and Inverse

**Finding the Determinant of a 2 x 2 Matrix**

The determinant of a matrix is a very important value that will help us later on when we are finding the inverse of a matrix, and when solving systems of linear equations.

The determinant of a matrix *C *is shown using **det *** C *or

**|C|.**

To find the determinant of a 2 x 2 matrix:

As you can see in the image, you simply **add the products of the diagonals.**

**Example:**

Therefore, the determinant of A is **-49.**

**Finding the Inverse of a 2 x 2 Non-Singular Matrix**

The inverse of a matrix can only be found if that matrix is **non-singular **and **square. **That is, if the **determinant of the matrix is not equal to zero **and the number of rows is equal to the number of columns**. **

This is how you find the inverse of a non-singular 2x2 matrix:

In the first part of the answer, we find the reciprocal of the determinant. Then, we switch the places of the *a *and *d *terms and make the *b *and *c *terms negative (this is a shortcut to finding a term called the **adjoint**). By multiplying these two terms together, we find our inverse.

For example:

However, this only works for 2 x 2 matrices. There is another method that works for all matrices (CSEC will only give you problems involving the determinant for 2 x 2 matrices though, so it is unnecessary to learn this other method. You can __read up on it here __if you want to, though).